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Identifier

St001318: Graphs ⟶ ℤ

Values

([],1) => 1

([],2) => 2

([(0,1)],2) => 2

([],3) => 3

([(1,2)],3) => 3

([(0,2),(1,2)],3) => 3

([(0,1),(0,2),(1,2)],3) => 2

([],4) => 4

([(2,3)],4) => 4

([(1,3),(2,3)],4) => 4

([(0,3),(1,3),(2,3)],4) => 4

([(0,3),(1,2)],4) => 4

([(0,3),(1,2),(2,3)],4) => 4

([(1,2),(1,3),(2,3)],4) => 3

([(0,3),(1,2),(1,3),(2,3)],4) => 3

([(0,2),(0,3),(1,2),(1,3)],4) => 3

([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3

([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

([],5) => 5

([(3,4)],5) => 5

([(2,4),(3,4)],5) => 5

([(1,4),(2,4),(3,4)],5) => 5

([(0,4),(1,4),(2,4),(3,4)],5) => 5

([(1,4),(2,3)],5) => 5

([(1,4),(2,3),(3,4)],5) => 5

([(0,1),(2,4),(3,4)],5) => 5

([(2,3),(2,4),(3,4)],5) => 4

([(0,4),(1,4),(2,3),(3,4)],5) => 5

([(1,4),(2,3),(2,4),(3,4)],5) => 4

([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 4

([(1,3),(1,4),(2,3),(2,4)],5) => 4

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4

([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 4

([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4

([(0,4),(1,3),(2,3),(2,4)],5) => 5

([(0,1),(2,3),(2,4),(3,4)],5) => 4

([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 4

([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 3

([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => 4

([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 4

([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => 4

([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 4

([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => 3

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => 3

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

([],6) => 6

([(4,5)],6) => 6

([(3,5),(4,5)],6) => 6

([(2,5),(3,5),(4,5)],6) => 6

([(1,5),(2,5),(3,5),(4,5)],6) => 6

([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 6

([(2,5),(3,4)],6) => 6

([(2,5),(3,4),(4,5)],6) => 6

([(1,2),(3,5),(4,5)],6) => 6

([(3,4),(3,5),(4,5)],6) => 5

([(1,5),(2,5),(3,4),(4,5)],6) => 6

([(0,1),(2,5),(3,5),(4,5)],6) => 6

([(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 6

([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(2,4),(2,5),(3,4),(3,5)],6) => 5

([(0,5),(1,5),(2,4),(3,4)],6) => 6

([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 5

([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 6

([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 6

([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 5

([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 5

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 5

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 5

([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 4

([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 5

([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,4),(2,3)],6) => 6

([(1,5),(2,4),(3,4),(3,5)],6) => 6

([(0,1),(2,5),(3,4),(4,5)],6) => 6

([(1,2),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 6

([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 5

([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => 5

([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 5

([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 4

([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 4

([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => 5

([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 5

([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 5

([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => 5

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Description

The number of vertices of the largest induced subforest with the same number of connected components of a graph.

Code

def statistic(G):
    n = G.num_verts()
    c = G.connected_components_number()
    for k in range(n,0,-1):
        for S in Subsets(G.vertices(), k):
            H = G.subgraph(S)
            if H.is_forest() and H.connected_components_number() == c:
                return k

Created

Dec 16, 2018 at 00:46 by Martin Rubey

Updated

Dec 16, 2018 at 00:46 by Martin Rubey